Black holes with a null Killing vector in three-dimensional massive gravity

TL;DR

This work analyzes three-dimensional new massive gravity (NMG) with two commuting Killing vectors, one null, to construct and classify black hole solutions. By reducing the field equations to a master equation for an AdS-wave–type ansatz, the authors obtain a family $F( ho) = a_+ ho^{p_+} + a_- ho^{p_-} + d$ with $p_\pm = \frac{1 \pm \sqrt{m^2 l^2 + 1/2}}{2}$ and identify three critical couplings $m^2 l^2 = 17/2$, $7/2$, and $1/2$ that yield regular black holes. They compute entropy, mass, and angular momentum via Wald and ADT formalisms, finding a null warped class (massless with nonzero $J$), two other zero-$M$/$J$ cases, and a logarithmic AdS$_3$-asymptotic family with a continuum of states above the extreme BTZ ground state; these results echo log gravity phenomena seen in TMG and raise questions about the consistency of NMG at the critical coupling $m^2 l^2 = 1/2$. The work thus reveals a rich spectrum of black hole solutions in NMG and motivates further study of their holographic and thermodynamic properties.

Abstract

We investigate solutions of new massive gravity with two commuting Killing vectors, one of which is null, with a special emphasis on black hole solutions. Besides extreme BTZ black holes and, for a special value of the coupling constant, massless null warped black holes, we also obtain for a critical coupling a family of massive "log" black holes. These are asymptotic to the extreme BTZ black holes in the sense of log gravity.